An inverse problem in radiation therapy.

The mathematical formalism associated with a 2-dimensional inverse problem in radiation therapy treatment and planning is discussed. The formalism is extended to convex phantoms of arbitrary cross-section. Relations necessary to produce circularly symmetric dose distributions about any point within the phantom are obtained. The general case for a particularly simple class of ideal dose distributions within 2-dimensional convex phantoms of arbitrary shape is solved. The relationship between treatment beans with and without negative fluences, and their associated dose distributions, is discussed.

The verification of an inverse problem in radiation therapy.

The inverse problem in radiation therapy presents a solution for a fluence distribution based on the specification of a region of dose in a patient. We show results for one such solution based on the inversion of an integral over a function of the fluence profile of a rotating beam. We use Monte Carlo methods and numerical integrations to evaluate dose distributions obtained with the inverse method and show the limitations of this theoretical approach. Our results show that dose to a single circular region at an arbitrary position in a 2-dimensional volume can be calculated. Uniform dose to arbitrarily shaped regions cannot be calculated with this formalism, although practical solutions can still be obtained.

Stereotaxic localization of intracranial targets.

We report on a useful clinical method for precisely locating intracranial targets. Utilizing the BRW system, the technique is currently used in stereotaxic irradiation of arteriovenous malformations. An intracranial localizer box, with four radio-opaque markers on each face, surrounds the patient's head and is attached to the BRW Head Ring. Two localization films are required. One film includes the target and the eight anterior and posterior markers, whereas the other film includes the target and the eight right and left markers. There are no constraints that the films be orthogonal or parallel to the box faces, only that the target and radio-opaque markers appear on the films. In addition, knowledge of the source-image and source-target distances are not required. Analysis of the projected target and radio-opaque markers gives both the target location and magnification. Simulation with the BRW Phantom Base demonstrates that point targets can be located with respect to the BRW system to within 0.3 mm and magnification determined to within 0.5%.

Radiosurgery for arteriovenous malformations of the brain using a standard linear accelerator: rationale and technique.

We have recently initiated a program for irradiating small, unresectable arteriovenous malformations (AVM's) in the brain. The treatments are delivered using a modified and carefully calibrated 6 MV linac. We are using high, single doses (15 to 25 Gy) with a goal of sclerosing the vessels and preventing hemorrhages. This technique, radiosurgery, is somewhat controversial in the radiotherapy community. Since the treatment is given in a single sitting, rather than in the more conventional pattern of multiple small daily fractions, there is some concern about late radiation damage to the normal brain tissue. However an extensive review of the literature leads us to the conclusion that if a technique is used that keeps the volume irradiated to high dose small, radiosurgery is a safe and efficacious treatment for small (less than 2.5 cm) AVM's. To decrease the risk of necrosis of normal brain tissue, it is important to confine the high dose region as tightly as possible to the target volume. Precise target localization and patient immobilization is achieved using a stereotactic head frame which is used during angiography, CT scanning, and during the radiation treatment. This minimizes the margin of safety that must be added to the target volume for errors in localization and set-up. The treatment is delivered using multiple noncoplanar arcs, with small, sharp edged X ray beams, and with the center of the AVM at isocenter. This produces a rapid dropoff of dose beyond the target volume. Early results in our first few patients are encouraging.